Statistical Analysis of Laboratory Data Using PCA and LDA Techniques
Explore the statistical analysis of laboratory data employing Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). The data includes variables like alkaline phosphatase (alkfos) levels, grouped data, complete cases analysis, and prediction of group classifications. Visualizations and interpretations of variances are also presented.
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alkfos PCA SPH 247 Statistical Analysis of Laboratory Data
> library(ISwR) > data(alkfos) > names(alkfos) [1] "grp" "c0" "c3" "c6" "c9" "c12" "c18" "c24 > summary(alkfos) grp c0 c3 c6 Min. :1.000 Min. : 81.0 Min. : 79.0 Min. : 79.0 1st Qu.:1.000 1st Qu.:124.0 1st Qu.:110.0 1st Qu.:112.5 Median :1.000 Median :161.0 Median :134.0 Median :146.0 Mean :1.465 Mean :159.9 Mean :143.3 Mean :149.0 3rd Qu.:2.000 3rd Qu.:190.5 3rd Qu.:170.5 3rd Qu.:167.5 Max. :2.000 Max. :237.0 Max. :277.0 Max. :298.0 c9 c12 c18 c24 Min. : 74.0 Min. : 73.0 Min. : 69.0 Min. : 68.0 1st Qu.:107.5 1st Qu.:103.0 1st Qu.:114.0 1st Qu.:111.8 Median :140.5 Median :134.0 Median :140.0 Median :146.5 Mean :140.3 Mean :143.3 Mean :149.1 Mean :150.1 3rd Qu.:163.5 3rd Qu.:168.0 3rd Qu.:185.5 3rd Qu.:189.8 Max. :240.0 Max. :289.0 Max. :288.0 Max. :260.0 NA's : 1.0 NA's : 2.0 NA's : 4.0 NA's : 5.0 May 7, 2010 SPH 247 Statistical Analysis of Laboratory Data 2
> af1 <- alkfos[complete.cases(alkfos),] > afmat <- af1[,-1] > grp <- af1$grp > pca.af <- prcomp(afmat,scale=T) > pca.tam <- prcomp(afmat[grp==2,],scale=T) > pca.placebo <- prcomp(afmat[grp==1,],scale=T) > plot(pca.af$x[,1:2],col=grp) > plot(pca.af) May 7, 2010 SPH 247 Statistical Analysis of Laboratory Data 3
2 1 PC2 0 -1 -4 -2 0 2 4 May 7, 2010 SPH 247 Statistical Analysis of Laboratory Data 4 PC1
pca.af 5 4 Variances 3 2 1 0 May 7, 2010 SPH 247 Statistical Analysis of Laboratory Data 5
> library(MASS) > lda.af <- lda(afmat,grp) > lda.af Prior probabilities of groups: 1 2 0.6 0.4 Group means: c0 c3 c6 c9 c12 c18 c24 1 156.7143 161.8571 173.9048 158.4286 163.8571 164.3333 163.2857 2 164.2143 125.1429 123.7143 118.7143 117.2857 130.7857 134.8571 Coefficients of linear discriminants: LD1 c0 0.0618073455 c3 -0.0329471378 c6 0.0004421163 c9 -0.0232320119 c12 -0.0248954902 c18 0.0113410946 c24 0.0003473940 May 7, 2010 SPH 247 Statistical Analysis of Laboratory Data 6
> af.pred <- predict(lda.af) > table(af.pred$class,grp) grp 1 2 1 20 0 2 1 14 > plot(grp,af.pred$x) May 7, 2010 SPH 247 Statistical Analysis of Laboratory Data 7
4 2 af.pred$x 0 -2 1.0 1.2 1.4 1.6 1.8 2.0 grp May 7, 2010 SPH 247 Statistical Analysis of Laboratory Data 8
